Three lectures on classical integrable systems and gauge field theories
High Energy Physics - Theory
2009-11-13 v1
Abstract
In these lectures I consider the Hitchin integrable systems and their relations with the self-duality equations and the twisted super-symmetric Yang-Mills theory in four dimension follow Hitchin and Kapustin-Witten. I define the Symplectic Hecke correspondence between different integrable systems. As an example I consider Elliptic Calogero-Moser system and integrable Euler-Arnold top on coadjoint orbits of the group GL(N,C) and explain the Symplectic Hecke correspondence for these systems.
Cite
@article{arxiv.0802.3857,
title = {Three lectures on classical integrable systems and gauge field theories},
author = {M. Olshanetsky},
journal= {arXiv preprint arXiv:0802.3857},
year = {2009}
}
Comments
36 pages, Lectures given at Advanced Summer School on Integrable Systems and Quantum Symmetries (Prague, June, 2007)